2x(12x+1)=1

Solution for 2x(12x+1)=1 equation:

Simplifying
2x(12x + 1) = 1

Reorder the terms:
2x(1 + 12x) = 1
(1 * 2x + 12x * 2x) = 1
(2x + 24x2) = 1

Solving
2x + 24x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 2x + 24x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 2x + 24x2 = 0

Factor a trinomial.
(-1 + -4x)(1 + -6x) = 0

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25
Subproblem 2
Set the factor '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {-0.25, 0.1666666667}